The Construction of Curves and Surfaces Using Numerical Optimization Techniques

Numerical optimization techniques are playing an increasing role in curve and surface construction. Often difficult problems in curve and surface construction, especially when some aspect of shape control is involved, can be phrased as a constrained optimization problem. Four such classes of problems are explored: parametric curve fitting with non-linear shape constraints; explicit surface fitting with linear shape constraints; surface fitting to scattered data giving rise to ill-posed problems; finally, variable knot problems. In each of these problems there is a nonlinear aspect: either the shape of the curve or surface is important for manufacturing or engineering reasons or the shape affects the convergence of numerical algorithms which use the curve or surface or the placement of knots affects the accuracy of the fits. In all cases the class of functions used is that of parametric spline curves and tensor or direct product spline surfaces. The reason for choosing this class is that splines provide flexible models that are easily evaluated and stored. Furthermore, the B-spline representation of splines leads to convenient expressions for shape control over regions

Hedge funds and systemic risk.

A hedge fund is a privately offered investment vehicle that pools the contributions of investors in order to invest in a variety of assets, such as securities, futures, options, bonds and currencies. Hedge funds have attracted growing attention from policy makers, financial market participants and the general public due to their rapid growth and substantial scale, their importance to banks as clients and the impact of their trading activity on global capital markets. Because of their rapid growth and the market disruptions caused by Long-Term Capital Management (LTCM) in 1998, some analysts believe that hedge funds pose systemic risks. However, this is unlikely. A thorough review of the avenues through which hedge funds could cause systemic problems indicates that, although a major disruption emanating from the hedge fund sector is possible, it would be diffi cult for the sector to be highly disruptive to fi nancial markets. Post-LTCM, regulatory authorities have encouraged banks to monitor their hedge fund clients through constraints on their leverage. This has thus far proven effective, as the recent failure of Amaranth demonstrates. That failure, the largest yet, caused hardly a ripple in the wider financial markets. Hedge funds support the robustness of markets in many ways. They provide attractive investment alternatives and improve economy-wide risk sharing. In addition, they promote fi nancial market stability by assuming risks that other market participants are unwilling or unable to bear; by providing liquidity; and by placing trades that move mispriced assets toward their “fundamental” values. Of course, hedge funds could raise problems through their dominant role in some markets, active trading strategies, use of leverage and relative lack of transparency. Counterparties must therefore be cognizant of the risks they bear from hedge funds. Also, regulators must continue to promote better hedge fund risk management and transparency through their regulation of counterparties while remaining vigilant about potential systemic risks emanating from the sector. On balance, however, hedge funds enhance market stability and are unlikely to be the source of a systemic failure.

Field Driven Thermostated System : A Non-Linear Multi-Baker Map

In this paper, we discuss a simple model for a field driven, thermostated random walk that is constructed by a suitable generalization of a multi-baker map. The map is a usual multi-baker, but perturbed by a thermostated external field that has many of the properties of the fields used in systems with Gaussian thermostats. For small values of the driving field, the map is hyperbolic and has a unique SRB measure that we solve analytically to first order in the field parameter. We then compute the positive and negative Lyapunov exponents to second order and discuss their relation to the transport properties. For higher values of the parameter, this system becomes non-hyperbolic and posseses an attractive fixed point.Comment: 6 pages + 5 figures, to appear in Phys. Rev.

Measurements of Surface Diffusivity and Coarsening During Pulsed Laser Deposition

Pulsed Laser Deposition (PLD) of homoepitaxial SrTiO3 was studied with in-situ x-ray specular reflectivity and surface diffuse x-ray scattering. Unlike prior reflectivity-based studies, these measurements access both the time- and the length-scales of the evolution of the surface morphology during growth. In particular, we show that this technique allows direct measurements of the diffusivity for both inter- and intra-layer transport. Our results explicitly limit the possible role of island break-up, demonstrate the key roles played by nucleation and coarsening in PLD, and place an upper bound on the Ehrlich-Schwoebel (ES) barrier for downhill diffusion

Online learning : towards enabling choice

Education is rapidly evolving from an opportunity that was provided mainly for an elite to one that is available to a mass markets and as such is prone to the forces generated by this environment. Where, in the established pattern, commercial interest was limited mainly to the use of skills developed during the educational process, the future model of educational provision will involve extensive commercial activity in the production, delivery and marketing of material. Already there are a number of commercial companies offering framework products enabling "off the shelf solutions" for the construction and delivery of web based courses in any subject area. The commercialisation of education is underway and it is inevitable that it will be viewed, by entrepreneurs and customers alike, as any other commercial product. It would seem reasonable that the consumer should be able to evaluate the performance of these new modes of working in a similar manner to other commercial products. This paper draws together current thinking on the problems associated with evaluating computer and communication based learning

Analysis of the wind tunnel test of a tilt rotor power force model

Two series of wind tunnel tests were made to determine performance, stability and control, and rotor wake interaction on the airframe, using a one-tenth scale powered force model of a tilt rotor aircraft. Testing covered hover (IGE/OCE), helicopter, conversion, and airplane flight configurations. Forces and moments were recorded for the model from predetermined trim attitudes. Control positions were adjusted to trim flight (one-g lift, pitching moment and drag zero) within the uncorrected test data balance accuracy. Pitch and yaw sweeps were made about the trim attitudes with the control held at the trimmed settings to determine the static stability characteristics. Tail on, tail off, rotors on, and rotors off configurations were testes to determine the rotor wake effects on the empennage. Results are presented and discussed

BulB - visualizing bulletin board activity

Visualisation is well known as an effective means of enriching user interaction with complex systems. Recent research with online communities has considered the application of visualisation tool support, with the intention of further improving communication between community members. This paper reviews existing work in this area with specific reference to the application of visualisation to improve user interaction within online forums such as bulletin boards. The paper then outlines work undertaken by the authors to develop a second-generation visualisation tool - 'BulB'